Global Generation of Adjoint Line Bundles on Projective $5$-folds

Fei Ye; Zhixian Zhu

Global Generation of Adjoint Line Bundles on Projective $5$-folds

Algebraic Geometry 2016-12-05 v2

Authors: Fei Ye , Zhixian Zhu

Abstract

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$ . We show that $\mathcal{O}_X(K_X+L)$ is globally generated.

Keywords

adjoint line bundles projective 5-folds global generation ample line bundle smooth projective variety canonical divisor

Cite

@article{arxiv.1405.0678,
  title  = {Global Generation of Adjoint Line Bundles on Projective $5$-folds},
  author = {Fei Ye and Zhixian Zhu},
  journal= {arXiv preprint arXiv:1405.0678},
  year   = {2016}
}

Comments

Final version to appear in manuscripta mathematica. We notice that mistakes were introduced by the journal to some fractions in the form "expression/expression" which should be read as "(expression)/(expression)"

Global Generation of Adjoint Line Bundles on Projective $5$-folds

Abstract

Keywords

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